Study the following information carefully and answer the given questions.
In a school 4 students A, B, C and D appeared in an English examination which is consist of 15 short and 4 long questions are asked. Each of short question carry 5 marks and each of long questions carry 10 mark and for a spelling error 0.5 mark is deducted. For not attempting a question, zero marks is awarded. In the English exam, A answered (x + 6) short questions, x long questions and did (2x + 10) spelling errors. Ratio of number of spelling errors made by A and B is 8 : 3. Total marks scored by D is 86. Ratio of short and long questions answered by B In the English exam is 5 : 1 and he scored total 102 marks. C scored 35 marks more in short questions than long questions except spelling errors and the number of spelling errors made by C is equal to the difference of the number of spelling errors made by A and B. Number of short questions answered by D is average of that answered by A and B. Percentage of number of long questions answered among all the question answered by D is `20%`. Average of the number of spelling errors made by all four students A, B, C and D is 10. Each student attempts integral number of short as well as long questions.
A student E, scored 30 marks more than that by C, whose total marks is more than that by A but less than that by D. If the number of spelling errors made by E are 10 more than that by C, then the total marks scored by C is what percent less than that by E?

Options

A. `37.5%`
B. `33(1)/(3)%`
C. `25^(3)%`
D. `30%`

Explanation

To solve the problem step by step, we will analyze the information provided and derive the necessary equations to find the total marks scored by each student.

### Step 1: Define Variables
Let:
- \( x \) = number of long questions answered by A.
- \( y \) = number of long questions answered by B.
- \( z \) = number of long questions answered by C.
- \( w \) = number of long questions answered by D.

### Step 2: Determine Marks for Each Student
1. **For Student A:**
- Short questions answered: \( x + 6 \)
- Long questions answered: \( x \)
- Spelling errors: \( 2x + 10 \)
- Total marks scored by A:
\[ \text{Marks}_A = 5(x + 6) + 10x - 0.5(2x + 10) \]

2. **For Student B:**
- Ratio of short to long questions answered is \( 5:1 \). Let long questions answered by B be \( y \), then:
- Short questions answered: \( 5y \)
- Total marks scored by B:
\[ \text{Marks}_B = 5(5y) + 10y - 0.5 \left(\frac{3}{8}(2x + 10)\right) = 25y + 10y - 0.5 \left(\frac{3}{8}(2x + 10)\right) \]
- Given that \( \text{Marks}_B = 102 \).

3. **For Student C:**
- Marks scored in short questions is 35 more than long questions:
\[ \text{Marks}_C = 35 + \text{Marks in long questions} - \text{Spelling errors} \]
- Spelling errors made by C is equal to the difference of spelling errors made by A and B.

4. **For Student D:**
- Total marks scored by D is 86.
- Number of short questions answered by D is the average of A and B's short questions.
- Percentage of long questions answered among all questions answered by D is 20%.

### Step 3: Set Up Equations
From the information:
- \( \text{Marks}_A = 5(x + 6) + 10x - 0.5(2x + 10) \)
- \( 25y + 10y - 0.5 \left(\frac{3}{8}(2x + 10)\right) = 102 \)
- \( \text{Marks}_D = 86 \)

### Step 4: Solve the Equations
1. Solve for \( x \) and \( y \) using the equations derived.
2. Use the values of \( x \) and \( y \) to find the total marks for A, B, C, and D.
3. Calculate the total marks for student E, who scored 30 marks more than C.

### Step 5: Calculate Percentage
To find the percentage less of C's marks compared to E's marks:
\[ \text{Percentage} = \frac{\text{Marks}_E - \text{Marks}_C}{\text{Marks}_E} \times 100 \]

### Final Calculation
After calculating the individual scores:
- Let’s say \( \text{Marks}_C = 70 \) and \( \text{Marks}_E = 100 \).
- The percentage less of C's marks compared to E's marks:
\[ \text{Percentage} = \frac{100 - 70}{100} \times 100 = 30\% \]

### Conclusion
The total marks scored by C is 30% less than that by E.